Each muscle fibre is closely surrounded by connective tissue.  This acts as a support for the muscle fibres and unites them to each other.   1) Each muscle fibres is surrounded by delicate connective tissue that is called the endomysium .  2) Individual fasciculi are enclosed by a stronger sheath of connective tissue called the perimysium .  3) The entire muscle is surrounded by connective tissue called the epimysium .   This is illustrated by the schematic diagram below.          1= perimysium, 2= endomysium, 3= fasciculus.      At the junction of a muscle with a tendon, the fibres of the endomysium, the perimysium and the epimysium become continuous with the fibres of the tendon.   First published on: 27 December 2016